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AP Statistics > Chapters 1 and 3 > Flashcards

Chapters 1 and 3 Flashcards

1
Q

What is Statistics?

A

The study of variability

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2
Q

What is Variability?

A
  • how things differ
  • –> it exists everywhere
  • –> statisticians pay close attention to differences
    ex. we all look and act differently
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3
Q

What are the two branches of AP Statistics?

A

Inferential and Descriptive

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4
Q

What are Descriptive Stats?

A

Used to describe the basic features of data in a study

ex. pictures, summaries such as mean, median, and mode, etc.

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5
Q

What are Inferential Stats?

A

uses a random sample of data taken from a population to describe/make inferences about the population (the big picture)
ex. tasting soup; take one sip to determine what the whole soup tastes like

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6
Q

Compare Descriptive and Inferential Stats

A
  • descriptive: explains the data you have

- inferential: uses that data to say something about an entire population

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7
Q

What is Data?

A

any collected info

ex. survey about liking pizza; yes, no, yes, yes, no…
ex. number of cookies eaten/minute: 5, 4, 6, 7, 3…

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8
Q

What is a Population?

A

the group we are interested in (sizes may vary)

ex. “all teens in the US” or “all AP Stat students in my school”

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9
Q

What is a Sample?

A

a subset of a population

  • taken to make inferences about a population
  • all statistics are calculated from samples
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10
Q

Compare Population to Sample

A

Populations: generally large
Samples: small subsets of the population; taken to make inferences about population

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11
Q

Compare Data to Statistics

A

Data: each bit of info is collected from subjects; summarized by mean, median, mode, etc.
Statistics: the descriptions/summaries used for SAMPLES (mean, median, range, etc.)

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12
Q

Compare Data to Parameters

A

Data: each bit of info is collected from subjects; summarized by mean, median, mode, etc.
Parameters: the descriptions/summaries used for POPULATIONS (mean, median, range, etc.)

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13
Q

What is a Parameter?

A

a numerical summary of a population

ex. mean, median, range

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14
Q

What is a Statistic?

A

a numerical summary of a sample

ex. mean, median, range

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15
Q

Average wait time at a Dunkin Donuts drive thru. Cars are randomly sampled. Average wait time = 3.2 minutes. Population Parameter? Statistic? Data? Parameter of Interest?

A

Population Parameter: the true wait time (we will never know/have)
Statistic: average wait time (3.2 minutes)
Parameter of Interest: Population Parameter
Data: Wait time of each car

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16
Q

Compare Data-Statistic-Parameter using Categorical example

A 
Data: individual measures
ex. meal preference: taco, pasta, burger, pizza, taco... 
Statistics and Parameters are summaries
ex. STAT: 42% of sample prefer tacos 
ex. PARA: 42% of population prefer tacos
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17
Q

Compare Data-Statistic-Parameter using Quantitative example

A

Data: individual measures
ex. how long a person can hold their breath (sec): 45, 64, 32, 68 (raw data)
Statistics and Parameters are summaries
ex. STAT: avg. breath-holding time of sample= 52.4 sec
ex. PARA: avg. breath-holding of pop. = 52.4 sec

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18
Q

What is a Census?

A

Information taken from each member of a population

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19
Q

Does a Census make sense?

A

a census works for small populations (Mr. Nystrom’s students); impossible for large populations (all US kids)

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20
Q

What is the difference between a Parameter and a Statistic?

A

Parameters come from Populations

Statistics come from Samples

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21
Q

If I take a random sample of 20 hamburgers from Five Guys and count the number of pickles on a bunch of them, and one of them had 9 pickles, then the 9 from that burger would be called ______?

A

A Datum or Data Value

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22
Q

If I take a random sample of 20 hamburgers from Five Guys and count the number of pickles on a bunch of them, and the average number of pickles was 9.5, then the 9.5 is considered a ______?

A

Statistic (it is a summary of a sample)

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23
Q

If I take a random sample of 20 hamburgers from Five Guys and count the number of pickles on a bunch of them, and I do this b/c I want to know the true average number of pickles on a burger at Five Guys, the true average number is called a ______?

A

Parameter; a one number summary of a population (aka the parameter of interest)

24
Q

What is the difference between a sample and a census?

A

Samples contain info from a small part of a population. A Census contains info from the entire population.

25
Q

Use the following words in one sentence: Population, Parameter, Census, Sample, Data, Statistics, Inference, Population of Interest

A

I was curious about a population parameter, but a census was to costly so I decided to choose a sample, collect some data, calculate a statistic and use it to make an inference about the population of interest.

26
Q

If you are tasting soup, then the flavor of each individual thing in the spoon is the ___, the entire spoon is a ____. The flavor of all that stuff together is like the ______ and you use that to ______ about the flavor of the entire pot of soup, which would be the ______.

A
  • The flavor of each individual thing in the spoon is DATA
  • The entire spoon is the SAMPLE
  • The flavor of all the stuff together is the STATISTIC
  • MAKE AN INFERENCE about the flavor of the whole pot of soup, which would be the PARAMETER
27
Q

What are Random Variables?

A

A variable whose possible values are of random phenomena

ex. hair color, height, weight, etc.

28
Q

What is the difference between Quantitative and Categorical Variables?

A

Quantitative variables are numerical (height, IQ, etc.)

Categorical variables are categories (eye color, favorite music genre, etc.)

29
Q

What is the difference between Quantitative and Categorical Data?

A

Quantitative: numerical
ex. measuring weight, data would be: 125, 155, 223, 178, 222, etc.
Categorical: categorical
ex. eye color: blue, brown, brown, brown, blue, green, etc. ; often uses words like yes and no

30
Q

What is the difference between Discrete and Continuous Variables?

A

Discrete can be counted (ex. number of cars sold) and are integers.
Continuous cannot be counted; usually measurements (ex. weight of a mouse: 4.344 oz.)

31
Q

What is a Quantitative Variable?

A

Numeric values

ex. height, age, number or cars sold, SAT score

32
Q

What is a Categorical Variable?

A

Categories

ex. blonde, listens to hip hop, female, yes, no

33
Q

What do we sometimes call a Categorical Variable?

A

Qualitative

34
Q

What is Quantitative Data?

A

The actual numbers gathered from each subject: 211 lbs., 67 bpm, etc.

35
Q

What is Categorical Data?

A

The actual individual category from a subject, like “blue”, “female”, or “sophomore”.

36
Q

What is a Random Sample?

A

Randomly choosing subjects from a population.
Ex. rolling dice, choosing names from a hat, etc.
A real random sample requires external help (humans cannot do this on their own)

37
Q

What is Frequency?

A

How often something comes up.

38
Q

Data or Datum?

A

Datum is singular (collecting datum from a rat)

Data is plural (collecting data from a group of rats)

39
Q

What is a Frequency Distribution?

A

A table or a chart that shows how often certain values or categories occur in a data set.

40
Q

What is meant by Relative Frequency?

A

The PERCENT of times something comes up (frequency/total)

41
Q

How do you find Relative Frequency?

A

Divide frequency by the Total

42
Q

What is meant by Cumulative Frequency?

A

Add up the frequencies as you go down the table

Ex. selling candy; sell 10 in hour 1, then 5, 3, and 7. Cumulative Frequency is 10, 15, 18, 25

43
Q

Make a guess as to what Relative Cumulative Frequency is

A

The added up percentages
Ex. selling candy; sell 10 in hour 1, then 5, 3, and 7. Cumulative Frequency is 10, 15, 18, 25. Divide by the total giving percentages: 0.40. .60, .64, and 1.00.
–always end at 100%

44
Q

What is the difference between a Bar Chart and a Histogram?

A

Bar Charts are for categorical data (bars don’t touch)

Histograms are for quantitative data (bars touch)

45
Q

What is Mean?

A

Average; it is the balancing point of a histogram

46
Q

What is the difference between Population Mean and a Sample Mean?

A

Population Mean: mean of a population; a parameter

Sample Mean: mean of a sample; a statistic

47
Q

What symbols are used for Population and Sample Mean?

A

Mu ( ) for population mean

X-Bar ( ) for sample mean

48
Q

How can you think about the Mean and Median to remember the difference when looking at a histogram?

A

Mean is the balancing point of a histogram

Median splits the area of the histogram in half

49
Q

What is Median?

A

The number in the middle; splits area in half (always in the position n+1/2)

50
Q

What is Mode?

A

The most common values; peaks in a histogram.

51
Q

When do we often use Mode?

A

Categorical Variables

Ex. Describing average preference, we need to find what “most” students chose

52
Q

Why don’t we always use Mean?

A

It is not resilient; it is impacted by skewness and outliers

53
Q

When we say “The average teen”, are we talking about mean, median, or mode?

A

It depends; if it is height, it could be mean, if it is parental income, we would use median, if it is musical preference, we would use mode

54
Q

What is a clear example of where the mean would change but median wouldn’t? (this would show the mean’s resilience)

A

8 ppl. are asked how much they have in their wallet: {1,2,2,5,5,8,8,9}. Mean and median is 5. If one person just got back from casino and new set is {1,2,2,5,5,8,8,9000}. Median is still 5, but mean is over 1000.
–Median would be used as an average, not the mean (9000 is an outlier.)

55
Q

How are Mean, Median, and Mode positioned in a skewed left histogram?

A

Goes in order from left to right: Mean-Median-Mode

56
Q

How are Mean, Median, and Mode positioned in a skewed right histogram?

A

Goes in the opposite order: Mode-Median-Mean

57
Q

Who chases the tail?

A

The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean chases the tail… and outliers

AP Statistics (1 decks)

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